You can walk in straight form the ship, on a sunday many of the shops are shut but I found an interesting market to walk around and the cathedral is pretty spectacular but don't bother with the Norman Palace, you cant take pictures and if you are used to historic European buildings this will be a let down.
Although I only managed a few of the sites I preferred seeing a lot of a few rather than a glimpse of everything as I like to use my camera. if you are flying too and from Rome you can leave your bags at the airport and take a bus into town to se the sites
Managed to see Monte Carlo and Monaco on a quick walking tour. All the buses seem to stop at the Faronguard perfume factory for half an hour which just leaves half an hour to see the wonderful Medieval town of eve at the top of the hill above the factory. As my wife said the perfumery wasn't worth it I hiked straight up to Eze which is not for the unfit and even the hour I had wasn't enough but is better than the perfume factory.